Question: Solve for $x$ and $y$ using elimination. ${x+2y = 10}$ ${4x+5y = 34}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $-4$ ${-4x-8y = -40}$ $4x+5y = 34$ Add the top and bottom equations together. $-3y = -6$ $\dfrac{-3y}{{-3}} = \dfrac{-6}{{-3}}$ ${y = 2}$ Now that you know ${y = 2}$ , plug it back into $\thinspace {x+2y = 10}\thinspace$ to find $x$ ${x + 2}{(2)}{= 10}$ $x+4 = 10$ $x+4{-4} = 10{-4}$ ${x = 6}$ You can also plug ${y = 2}$ into $\thinspace {4x+5y = 34}\thinspace$ and get the same answer for $x$ : ${4x + 5}{(2)}{= 34}$ ${x = 6}$